Moreover, there are problems due to disturbing direct reflections which occur with reflective spatial light modulators due to reflection of the incident waves at the inter-pixel matrix.
It is known that in the Fourier plane the rectangular transmissive pixels exhibit an intensity distribution in the form of a sinc function of
                    -        sin            ⁢                          ⁢              c        ⁡                  (          x          )                      =                  sin        ⁡                  (                      π            ⁢                                                  ⁢            x                    )                            π        ⁢                                  ⁢        x              ,provided they are illuminated with coherent light. The higher diffraction orders expand at the side bands/side wings according to the scanning.
In their essay “Cross-talk analysis and reduction in fully parallel matrix-matrix multipliers”, Applied Optics, Vol. 34, No. 29, October 1995, p. 6752-6757, K. Raj and R. A. Athale describe an apodisation method of multiplicatively-coupled spatial light modulators, where analogue optical processors, which calculate a product of the matrices of two spatial light modulators, are analysed as regards cross-talk. It was found that the side bands of the sinc function in the Fourier plane, which correspond with the individual pixels of the spatial light modulator, are the main cause for cross-talk. Cross-talk can be reduced mainly by using an apodisation function for the individual pixels in the spatial light modulator. Pixel-wise apodisation is performed using an apodisation-function-containing mask, which is disposed immediately in front of the spatial light modulator, seen in the direction of light propagation.
A specialty is the fact that it is an apodisation of multiplicatively-coupled spatial light modulators, where the spatial light modulators are disposed one behind another in an optical path which passes through both spatial light modulators, said optical path also containing the illumination of the mask which comprises the apodisation function. Moreover, the arrangement of the apodisation mask immediately in front of the spatial light modulators is rather difficult to achieve.
A method for apodisation by way of illumination is known from the essay “Pixel image analysis of light valve projector considering apodisation caused by illumination” by S. Shikama, H. Suzuki, T. Endo and A. Sekiguchi, published in Opt. Eng. 43(6), June 2004, p. 1378-1380, according to which the apodisation is to be performed in the entrance pupil of an optical projection system in a light projector. The apodisation is here performed for the pupil of the optical system, but not for the object to be transformed:the pixel matrix of the spatial light modulator.
In their essay “Wave-front reconstruction by adding modulation capabilities of two liquid crystal devices”, Opt. Eng. 43(11), November 2004, p. 2650-2657, R. Tudela, E. Martin-Badosa, I. Labastida and A. Carnicer describe a method of additive coupling of two liquid crystal displays for wave-front reconstruction, where the additive superposition of wave fronts encoded in the spatial light modulators is achieved with the help of a beam splitter element. One drawback is that although there is an additive superposition of the spatial light modulators, the apodisation of the pixel arrays does not play a role.
In their essay “Electro-holographic display using 15 mega pixels LCD”, SPIE Vol. 2652/15, K. Maeno, N. Fukaya, O. Nishikawa et al. describe an electroholographic display, where an increase of the resolution of the spatial light modulators used for encoding the hologram is to be achieved by way of arranging side by side (tiling) several spatial light modulators in one dimension or two dimensions. In this particular electroholographic display five LCD panels are arranged side by side. Increasing the size of the entire display causes problems in particular with the optical systems which are required for Fourier transformation of the information encoded on the display. Moreover, totally gapless tiling is not possible, so that there are discontinuities in the encoded information.